<!DOCTYPE html>

<html>
  <head>
    <meta charset="utf-8">
    
    <title>Optionally Scipy-accelerated routines (numpy.dual) &mdash; NumPy v1.18 Manual</title>
    
    <link rel="stylesheet" type="text/css" href="../_static/css/spc-bootstrap.css">
    <link rel="stylesheet" type="text/css" href="../_static/css/spc-extend.css">
    <link rel="stylesheet" href="../_static/scipy.css" type="text/css" >
    <link rel="stylesheet" href="../_static/pygments.css" type="text/css" >
    <link rel="stylesheet" href="../_static/graphviz.css" type="text/css" >
    
    <script type="text/javascript">
      var DOCUMENTATION_OPTIONS = {
        URL_ROOT:    '../',
        VERSION:     '1.18.1',
        COLLAPSE_INDEX: false,
        FILE_SUFFIX: '.html',
        HAS_SOURCE:  false
      };
    </script>
    <script type="text/javascript" src="../_static/jquery.js"></script>
    <script type="text/javascript" src="../_static/underscore.js"></script>
    <script type="text/javascript" src="../_static/doctools.js"></script>
    <script type="text/javascript" src="../_static/language_data.js"></script>
    <script type="text/javascript" src="../_static/js/copybutton.js"></script>
    <link rel="author" title="About these documents" href="../about.html" >
    <link rel="index" title="Index" href="../genindex.html" >
    <link rel="search" title="Search" href="../search.html" >
    <link rel="top" title="NumPy v1.18 Manual" href="../index.html" >
    <link rel="up" title="Routines" href="routines.html" >
    <link rel="next" title="Mathematical functions with automatic domain (numpy.emath)" href="routines.emath.html" >
    <link rel="prev" title="numpy.maximum_sctype" href="generated/numpy.maximum_sctype.html" > 
  </head>
  <body>
<div class="container">
  <div class="top-scipy-org-logo-header" style="background-color: #a2bae8;">
    <a href="../index.html">
      <img border=0 alt="NumPy" src="../_static/numpy_logo.png"></a>
    </div>
  </div>
</div>


    <div class="container">
      <div class="main">
        
	<div class="row-fluid">
	  <div class="span12">
	    <div class="spc-navbar">
              
    <ul class="nav nav-pills pull-left">
        <li class="active"><a href="https://numpy.org/">NumPy.org</a></li>
        <li class="active"><a href="https://numpy.org/doc">Docs</a></li>
        
        <li class="active"><a href="../index.html">NumPy v1.18 Manual</a></li>
        

          <li class="active"><a href="index.html" >NumPy Reference</a></li>
          <li class="active"><a href="routines.html" accesskey="U">Routines</a></li> 
    </ul>
              
              
    <ul class="nav nav-pills pull-right">
      <li class="active">
        <a href="../genindex.html" title="General Index"
           accesskey="I">index</a>
      </li>
      <li class="active">
        <a href="routines.emath.html" title="Mathematical functions with automatic domain (numpy.emath)"
           accesskey="N">next</a>
      </li>
      <li class="active">
        <a href="generated/numpy.maximum_sctype.html" title="numpy.maximum_sctype"
           accesskey="P">previous</a>
      </li>
    </ul>
              
	    </div>
	  </div>
	</div>
        

	<div class="row-fluid">
      <div class="spc-rightsidebar span3">
        <div class="sphinxsidebarwrapper">
  <h3><a href="../contents.html">Table of Contents</a></h3>
  <ul>
<li><a class="reference internal" href="#">Optionally Scipy-accelerated routines (<code class="xref py py-mod docutils literal notranslate"><span class="pre">numpy.dual</span></code>)</a><ul>
<li><a class="reference internal" href="#linear-algebra">Linear algebra</a></li>
<li><a class="reference internal" href="#fft">FFT</a></li>
<li><a class="reference internal" href="#other">Other</a></li>
</ul>
</li>
</ul>

  <h4>Previous topic</h4>
  <p class="topless"><a href="generated/numpy.maximum_sctype.html"
                        title="previous chapter">numpy.maximum_sctype</a></p>
  <h4>Next topic</h4>
  <p class="topless"><a href="routines.emath.html"
                        title="next chapter">Mathematical functions with automatic domain (<code class="xref py py-mod docutils literal notranslate"><span class="pre">numpy.emath</span></code>)</a></p>
<div id="searchbox" style="display: none" role="search">
  <h4>Quick search</h4>
    <div>
    <form class="search" action="../search.html" method="get">
      <input type="text" style="width: inherit;" name="q" />
      <input type="submit" value="search" />
      <input type="hidden" name="check_keywords" value="yes" />
      <input type="hidden" name="area" value="default" />
    </form>
    </div>
</div>
<script type="text/javascript">$('#searchbox').show(0);</script>
        </div>
      </div>
          <div class="span9">
            
        <div class="bodywrapper">
          <div class="body" id="spc-section-body">
            
  <div class="section" id="module-numpy.dual">
<span id="optionally-scipy-accelerated-routines-numpy-dual"></span><h1>Optionally Scipy-accelerated routines (<a class="reference internal" href="#module-numpy.dual" title="numpy.dual"><code class="xref py py-mod docutils literal notranslate"><span class="pre">numpy.dual</span></code></a>)<a class="headerlink" href="#module-numpy.dual" title="Permalink to this headline">¶</a></h1>
<p>Aliases for functions which may be accelerated by Scipy.</p>
<p><a class="reference external" href="https://www.scipy.org">Scipy</a> can be built to use accelerated or otherwise improved libraries
for FFTs, linear algebra, and special functions. This module allows
developers to transparently support these accelerated functions when
scipy is available but still support users who have only installed
NumPy.</p>
<div class="section" id="linear-algebra">
<h2>Linear algebra<a class="headerlink" href="#linear-algebra" title="Permalink to this headline">¶</a></h2>
<table class="longtable docutils align-default">
<colgroup>
<col style="width: 10%" />
<col style="width: 90%" />
</colgroup>
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.linalg.cholesky.html#numpy.linalg.cholesky" title="numpy.linalg.cholesky"><code class="xref py py-obj docutils literal notranslate"><span class="pre">cholesky</span></code></a>(a)</p></td>
<td><p>Cholesky decomposition.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/numpy.linalg.det.html#numpy.linalg.det" title="numpy.linalg.det"><code class="xref py py-obj docutils literal notranslate"><span class="pre">det</span></code></a>(a)</p></td>
<td><p>Compute the determinant of an array.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.linalg.eig.html#numpy.linalg.eig" title="numpy.linalg.eig"><code class="xref py py-obj docutils literal notranslate"><span class="pre">eig</span></code></a>(a)</p></td>
<td><p>Compute the eigenvalues and right eigenvectors of a square array.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/numpy.linalg.eigh.html#numpy.linalg.eigh" title="numpy.linalg.eigh"><code class="xref py py-obj docutils literal notranslate"><span class="pre">eigh</span></code></a>(a[, UPLO])</p></td>
<td><p>Return the eigenvalues and eigenvectors of a complex Hermitian (conjugate symmetric) or a real symmetric matrix.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.linalg.eigvals.html#numpy.linalg.eigvals" title="numpy.linalg.eigvals"><code class="xref py py-obj docutils literal notranslate"><span class="pre">eigvals</span></code></a>(a)</p></td>
<td><p>Compute the eigenvalues of a general matrix.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/numpy.linalg.eigvalsh.html#numpy.linalg.eigvalsh" title="numpy.linalg.eigvalsh"><code class="xref py py-obj docutils literal notranslate"><span class="pre">eigvalsh</span></code></a>(a[, UPLO])</p></td>
<td><p>Compute the eigenvalues of a complex Hermitian or real symmetric matrix.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.linalg.inv.html#numpy.linalg.inv" title="numpy.linalg.inv"><code class="xref py py-obj docutils literal notranslate"><span class="pre">inv</span></code></a>(a)</p></td>
<td><p>Compute the (multiplicative) inverse of a matrix.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/numpy.linalg.lstsq.html#numpy.linalg.lstsq" title="numpy.linalg.lstsq"><code class="xref py py-obj docutils literal notranslate"><span class="pre">lstsq</span></code></a>(a, b[, rcond])</p></td>
<td><p>Return the least-squares solution to a linear matrix equation.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.linalg.norm.html#numpy.linalg.norm" title="numpy.linalg.norm"><code class="xref py py-obj docutils literal notranslate"><span class="pre">norm</span></code></a>(x[, ord, axis, keepdims])</p></td>
<td><p>Matrix or vector norm.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/numpy.linalg.pinv.html#numpy.linalg.pinv" title="numpy.linalg.pinv"><code class="xref py py-obj docutils literal notranslate"><span class="pre">pinv</span></code></a>(a[, rcond, hermitian])</p></td>
<td><p>Compute the (Moore-Penrose) pseudo-inverse of a matrix.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.linalg.solve.html#numpy.linalg.solve" title="numpy.linalg.solve"><code class="xref py py-obj docutils literal notranslate"><span class="pre">solve</span></code></a>(a, b)</p></td>
<td><p>Solve a linear matrix equation, or system of linear scalar equations.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/numpy.linalg.svd.html#numpy.linalg.svd" title="numpy.linalg.svd"><code class="xref py py-obj docutils literal notranslate"><span class="pre">svd</span></code></a>(a[, full_matrices, compute_uv, hermitian])</p></td>
<td><p>Singular Value Decomposition.</p></td>
</tr>
</tbody>
</table>
</div>
<div class="section" id="fft">
<h2>FFT<a class="headerlink" href="#fft" title="Permalink to this headline">¶</a></h2>
<table class="longtable docutils align-default">
<colgroup>
<col style="width: 10%" />
<col style="width: 90%" />
</colgroup>
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.fft.fft.html#numpy.fft.fft" title="numpy.fft.fft"><code class="xref py py-obj docutils literal notranslate"><span class="pre">fft</span></code></a>(a[, n, axis, norm])</p></td>
<td><p>Compute the one-dimensional discrete Fourier Transform.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/numpy.fft.fft2.html#numpy.fft.fft2" title="numpy.fft.fft2"><code class="xref py py-obj docutils literal notranslate"><span class="pre">fft2</span></code></a>(a[, s, axes, norm])</p></td>
<td><p>Compute the 2-dimensional discrete Fourier Transform</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.fft.fftn.html#numpy.fft.fftn" title="numpy.fft.fftn"><code class="xref py py-obj docutils literal notranslate"><span class="pre">fftn</span></code></a>(a[, s, axes, norm])</p></td>
<td><p>Compute the N-dimensional discrete Fourier Transform.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/numpy.fft.ifft.html#numpy.fft.ifft" title="numpy.fft.ifft"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ifft</span></code></a>(a[, n, axis, norm])</p></td>
<td><p>Compute the one-dimensional inverse discrete Fourier Transform.</p></td>
</tr>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.fft.ifft2.html#numpy.fft.ifft2" title="numpy.fft.ifft2"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ifft2</span></code></a>(a[, s, axes, norm])</p></td>
<td><p>Compute the 2-dimensional inverse discrete Fourier Transform.</p></td>
</tr>
<tr class="row-even"><td><p><a class="reference internal" href="generated/numpy.fft.ifftn.html#numpy.fft.ifftn" title="numpy.fft.ifftn"><code class="xref py py-obj docutils literal notranslate"><span class="pre">ifftn</span></code></a>(a[, s, axes, norm])</p></td>
<td><p>Compute the N-dimensional inverse discrete Fourier Transform.</p></td>
</tr>
</tbody>
</table>
</div>
<div class="section" id="other">
<h2>Other<a class="headerlink" href="#other" title="Permalink to this headline">¶</a></h2>
<table class="longtable docutils align-default">
<colgroup>
<col style="width: 10%" />
<col style="width: 90%" />
</colgroup>
<tbody>
<tr class="row-odd"><td><p><a class="reference internal" href="generated/numpy.i0.html#numpy.i0" title="numpy.i0"><code class="xref py py-obj docutils literal notranslate"><span class="pre">i0</span></code></a>(x)</p></td>
<td><p>Modified Bessel function of the first kind, order 0.</p></td>
</tr>
</tbody>
</table>
</div>
</div>


          </div>
        </div>
          </div>
        </div>
      </div>
    </div>

    <div class="container container-navbar-bottom">
      <div class="spc-navbar">
        
      </div>
    </div>
    <div class="container">
    <div class="footer">
    <div class="row-fluid">
    <ul class="inline pull-left">
      <li>
        &copy; Copyright 2008-2019, The SciPy community.
      </li>
      <li>
      Last updated on Feb 20, 2020.
      </li>
      <li>
      Created using <a href="http://sphinx.pocoo.org/">Sphinx</a> 2.4.2.
      </li>
    </ul>
    </div>
    </div>
    </div>
  </body>
</html>